N.J. Stat. § 19:3-16
If such determination shall not have been made until after such candidate shall have been inducted into office, then upon a certified copy of the record of the determination being sent to the Attorney-General, it shall be his duty to institute appropriate proceedings for the vacation of such office where no other proceeding to the same purpose has been commenced.
If the record relates to the election of any candidate to the office of United States Senator, member of Congress, State Senator, or member of the General Assembly, the Attorney-General, instead of instituting appropriate proceedings for the vacation of the office, shall send the certified copy, within five days after the same is received by him, to the United States Senate, the House of Representatives, the State Senate or the General Assembly, as the case may be, if such United States Senate, House of Representatives, State Senate or General Assembly is then in session, and if not, then on the first day of such session.
N.J.S. § 19:3-16